Each week, a subcommittee of four individuals is formed from among the members of a committee...

Each week, a subcommittee of four individuals is formed from among the
members of a committee comprising seven individuals. Two subcommittee
members are then assigned to lead the subcommittee, one as chair and the
other as secretary.
Calculate the maximum number of consecutive weeks that can elapse without
having the subcommittee contain four individuals who have previously served
together with the same subcommittee chair. The answer is 140. Could you explain why? Thank you so much!

Solutions

Expert Solution

Assumption: The formation of the sub-committee is not made radomly, rather each possible combination is applied over consecutive weeks. Similarly, for a particular subcommittee, each ember becomes the chair in each repetition.

Now, there are possible sub-committees and for each of these, there are ways of selecting the chair. So without repeating the same sub-comitteewith saame member as its chair, there can at most be weeks.

orchestra answered 1 year ago

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